The table shows how much a painter charges for painting a home. Is the relationship shown linear?
Explain.
Hours worked
Amount charged
1
35
2
50
3
70
4
90
To determine if the relationship shown in the table is linear, we can analyze the changes in the "Amount charged" for each additional "Hour worked".
Looking at the data, we can see that the amount charged increases as the number of hours worked increases. However, the increase in the amount charged is not consistent. For example, the increase from 1 hour worked (charge of $35) to 2 hours worked (charge of $50) is an increase of $15. However, the increase from 2 hours worked to 3 hours worked is an increase of $20, and the increase from 3 hours worked to 4 hours worked is an increase of $20 again.
Since the rate of increase in the amount charged is not the same for each additional hour worked, the relationship shown is not linear.